PCR Modeling 2004.08.31 MEC Lim Hee Woong

Denaturation dsDNA conc. input Melting curve of known DNA conc. Temp. Keq output denaturation efficiency Released ssDNA conc. output

Melting Profile Sigmoid function assumption Parameters Tm: Melting temperature : Transition width: begin & end temperature Cinit: initial dsDNA concentration for melting profile Measured and fitted by experiment with UV spectrophotometer or real-time PCR machine

Equilibrium Constant Kd from Tm Profile

Denaturation Cds0: initial dsDNA strand in denature step Kd(T): equlibrium constant from melting profile

Annealing 경쟁적인 annealing반응, primer vs. template

Wetmur (Annu. Rev. Biophys. Bioeng. 1976) 다른 step (denaturation, extension)과는 달리 각 template에 대해forward와 backward를 구분 대칭성에 의해 forward와 backward strand의 농도변화는 같다고 가정 위의 계산식에 사용되는 Css, 와 Chd 는 forward 혹은 backward의 한쪽 방향 strand에 대한 농도 앞의 denaturation step에서 계산된 ssDNA의 농도의 절반 만큼의 농도를 할당하여 계산 수행하고 Annealing이 끝난 후 위 계산 결과에 2를 곱하여 backward/forward의 구분을 없앰 Rate constant k의 값을 몰라도 그 비율만으로 최종 product의 비율을 계산 가능 Wetmur (Annu. Rev. Biophys. Bioeng. 1976) Calculation Numerical method, Runge-Kutta formulae Matlab function “ode45”

Annealing 2 -Temperature Ramping- Pre-annealing Template Tm hdDNA Tm Competitive annealing Time Pre-annealing of template Competitive annealing to form dsDNA and hdDNA Tm,hdDNA<Tm,dsDNA Pre-annealing takes place before competitive annealing

Wetmur (Annu. Rev. Biophys. Bioeng. 1976)

Extension rt: t 초 후의 reaction rate From Hsu et al. BB 1997 rt: t 초 후의 reaction rate ke: extension rate for one polymerase knu: nucleotide incorporation rate of one polymerase Ea,t: t초 후에 실제 polymerization에 참가하는 enzyme의 농도

실제 polymerization에 참가하는 enzyme 의 농도 Active enzyme Cenz: thermal deactivate되지 않고 남아있는 polymerase 농도 Cenz를 hetero duplex부분과 template duplex부분의 비율로 나누어 실제 polymerization에 참가하는 enzyme의 비율을 구한다. 단순히 duplex의 농도만 고려하는 것이 아니라 duplex region의 길이까지도 고려함 Kainz (BBA 2000) paper 참조 Calculation Numerical method, Runge-Kutta formulae Matlab function “ode45”

Enzyme Deactivation From Hsu et al. BB 1997 Hsu et al. (BB, 1997) 논문의 deactivation 식에 temperature ramping을 추가하여 확장 at: remaining enzyme ratio after t second considering temperature ramping T1, T2, ∆t: ∆t초 동안 T1에서 T2로 온도가 변함 Calculation Numerical method, Runge-Kutta formulae Matlab function “ode45”

Product Flow

Simulation

9e-012  4.93815e-008

9e-013  4.28836e-008

9e-014  3.59484e-008

PCR Plateau? Figures from TAKARA When varying amounts of a single target are amplified, a constant maximum level of product is obtained. Coamplification of different concentrations of different targets results in retention of the initial proportions. Morrison et al. BBA, 1994

Factors of Plateau? Reduction in the denaturation efficiency Utilization of substrates (dNTPs or primers) Reannealing of specific product at concentrations above 10-8 M Thermal inactivation or limited concentration of DNA polymerase Exonuclease activity of Taq polymerase Inhibition of enzyme activity by increasing pyrophosphate

In Plateau In plateau What occurs at each step in plateau? Question… The template concentration reaches constant level (about 10-8 order), even if the order of initial concentration varies. What occurs at each step in plateau? Denaturation Constant denaturation efficiency and ssDNA concentration ≈ 1, almost perfect denaturation Not only in plateau Annealing Constant annealing efficiency and hdDNA concentration ≈ 0 or >> 0 ? Extension Constant extension efficiency Question… Annealing efficiency and the amount of hdDNA in plateau Extension efficiency in plateau What is the major factor for plateau

Other Insignificant Factors Mis-annealing of primers Reaction condition change pH change? MgCl2 concentration? DNA contaminants (non-specific products, primer-dimer)

Parameters to Fit Hybridization rate constant Extension rate constant Pre-annealing (?) region

Extension2 Michaelis-Menten Equation + BB paper